Question: A circle has a radius of $4$. An arc in this circle has a central angle of $207^\circ$. What is the length of the arc? ${8\pi}$ ${207^\circ}$ $\color{#DF0030}{\dfrac{23}{5}\pi}$ ${4}$
First, calculate the circumference of the circle. $c = 2\pi r = 2\pi (4) = 8\pi$ The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{207^\circ}{360^\circ} = \dfrac{s}{8\pi}$ $\dfrac{23}{40} = \dfrac{s}{8\pi}$ $\dfrac{23}{40} \times 8\pi = s$ $\dfrac{23}{5}\pi = s$